Missing number in sequence (numbers are in decending order)

string sentence = "600599598596";
//string sentence = "60595856";
int len = sentence.Length;
int half = len/2;
//here is a magic!
    var dividers =  Enumerable.Range(1, half).Where(i=>len%i==0).ToList();
foreach(int d in dividers)
{
    //create list of chars for later use
    List<int> numbers = new List<int>();
    //loop through the chars in sentence
    //[i] - counter
    int i = 0;
    do
    {
        //get number of chars accordingly  to the value stored in [d]
        string tmp = string.Join("", sentence.Skip(i).Take(d));
        //try parse string into integer
        //if possible, then add it to the list
        int number = 0;
        if (Int32.TryParse(tmp, out number)) numbers.Add(number);
        i+=d;
    } while (i<len);
    //find missing value
    var misVal = numbers.Zip(numbers.Skip(1), (first, second) => Tuple.Create(first, second, first-second-1))
        .Where(x=>x.Item3==1)
        .Select(x=> x.Item2+1)
        .FirstOrDefault();
    Console.WriteLine("For list: [{0}] missing value is: {1}", string.Join(";", numbers), misVal);
}

For list: [6;0;0;5;9;9;5;9;8;5;9;6] missing value is: 0
For list: [60;5;99;59;85;96] missing value is: 0
For list: [600;599;598;596] missing value is: 597
For list: [600599;598596] missing value is: 0

var misVal = numbers.Zip(numbers.Skip(1), (first, second) => Tuple.Create(first, second, first-second-1))
	.Where(x=>x.Item3==1)
	.Select(x=>x.Item2+1)
	.ToList();